# Parity conditions

Hello guys,

today in the Schewser mocks I have found this relationships:

For uncovered partiy: S(exp) = S0*(1+i_foregin)/(1+i_domestic)

For international FIsher relation: (1 + i_foreign)/(1 + i_domestic) = (1 + inflation_foregin)/(1+inflation_domestic)

Do you know where do they come from? I have studied on the curriculum and could not find them anywhere!

For uncovered : The expected return on a foreign investment must equal the return on a comparable domestic investment, thus :

(ExpS A/B) * (1 + i A) = (S A/B) * (1+ i B) =>(ExpS A/B) = (S A/B) * (1+ i B)/(1 + i A).

We can approximate by : %change (ExpS A/B) = iA - iB

For the international Fisher, i searched in schweser and didn’t find the formula you mentionned, did you mean :

iA - iB = Exp(Inflation A) - Exp(Inflation B)

No I mean the same as I wrote above, it’s in the 3rd practice test!

I guess that, from what you wrote above, also in the relative PPP %change = inflation A - inflation B is an approximation, so if you apply uncovered interest parity and relative PPP at the same time you obtain what they have reported on the mock solutions, but I am not sure about it

Sorry I meant the 3rd mock test (of the first series of 3 mocks)

Sorry I don’t have the schweser mock exams I don’t understand very well the mechanics behind economics (i just took the basics, and wrote the simplest formulas i could remember), but from what you said, Ex-ANTE PPP + Uncovered Parity leads to International Fisher effect if REAL Interest is the same and =0 (then the nominal interest differential is the inflation differential).

I know there is a chart in schweser (book 1 p.267) that outlines the links between them all.

If it can help, here is my formulas that i figured out :

• Covered parity : F / S = (1+ia)/(1+ib) => Forward premium/discount = ia - ib
• Uncovered parity : E(S) / S = (1+ia)/(1+ib) => E(%Change S) = ia - ib
• Absolute PPP : S = CPI(a) / CPI(b)
• Relative PPP : %Change S = infl-a - infl-b
• Ex-ante PPP : E(%Change S) = E(infl-a) - E(infl-b)
• International Fisher : ia - ib = E(infl-a) - E(infl-b) (if real rate =0)

Hope this helps !